Communication channel capacity estimation

ABSTRACT

Prediction of a channel-capacity is accomplished based on a TDR echo without explicitly estimating the topology of the line. The prediction is based on obtaining a measured TDR echo, determining a theoretical TDR echo for a plurality of loop lengths, estimating the equivalent TDR length based on an optimization, updating the equivalent TDR length and utilizing the updated TDR length to predict one or more of the upstream and downstream data rates.

RELATED APPLICATION DATA

This application claims the benefit of and priority under 35 U.S.C.§119(e) to U.S. Provisional Application No. 60/543,966, entitled“Equivalent Estimation Method for Evaluating Subscriber Lines Based OnTime Domain Reflectometry,” filed Feb. 11, 2004, which is incorporatedherein by reference in its entirety.

BACKGROUND

1. Field of the Invention

This invention generally relates to communication systems. Inparticular, an exemplary embodiment of this invention relates toestimating communication channel capacity. More particularly, anexemplary aspect of the present invention relates to estimating digitalcommunications channel capacity.

2. Description of Related Art

Digital Subscriber Line (DSL) technology makes it possible to transporthigh bit rate digital information via a communications channel, suchas-a subscriber line. The channel capacity, which is defined as theobtainable data rate for a given line, is based on the physicalstructure and topology of the line, such as the length of the line,gauge, existence of bridged taps, bridged tap locations and lengths,etc. Thus, if the topology of the line is known, the data rate can bepredicted prior to providing DSL service to a customer.

Time domain reflectometry (TDR) is a very useful tool for characterizinga subscriber line. TDR operates by sending an electrical pulse down theline and measuring the returned signal, referred to as a TDR echo. Themeasured TDR echo contains information about the physical structure andtopology of the line.

The most common method for evaluating the channel capacity from a TDRecho is by explicitly estimating the physical topology of the line basedon the transmission line theory, and then searching a database to find adata rate corresponding to the specific topology. One issue with thisapproach is the estimation complexity increases dramatically when thetopology of the line is complex. For example, consider a line with Nconsecutive sections of different gauges but without bridged taps. Sincethere are two variables that need to be estimated for each section, thegauge and the length, the searching space is 2N dimensional. Thus, thecomputation complexity increases exponentially with the number ofdistinct sections.

SUMMARY

The ultimate goal of estimating the topology of a subscriber line fromthe TDR echo is to evaluate the channel capacity of the line. Hence, ifone can estimate a line with a much simpler topology but the samechannel capacity as the actual line from the TDR echo, the goal can beachieved with much less computation complexity.

An exemplary embodiment of the present invention follows this theory,and provides a method of evaluating the channel capacity from the TDRecho without explicitly estimating the topology of the line.

For simplicity, herein a subscriber line without bridged tap is referredto as a straight line. Here “straight” means no bridged tap presented.Also, a subscriber line is referred to herein as a line, a loop or awire interchangeably.

An exemplary embodiment of the present invention is developed based ontransmission line theory. A typical transmission line system can beschematically represented as illustrated in FIG. 1, where V_(S) is theoutput voltage of the source, Z_(S) is the output impedance of thesource, Z_(L) is the input impedance of the load, and L is the length ofthe line connecting the source and the load. V_(S), Z_(S) and Z_(L) arefunctions of frequency. According to the transmission line theory, whenthe electrical wave generated by the source travels down to the line, itis attenuated by the line, and reflected whenever there is an impedancediscontinuity. The wave travels forward and backward inside the line toinfinity.

Assume the characteristic impedance and the propagation constant of agiven line to be Z₀ and δ, where Z₀ and δ are functions of frequency.With a straight loop with a single gauge, the only impedance changes are(1) at the connection between the source and the line, and (2) at theconnection between the line and the load. Assume the reflectioncoefficient, which is defined as the ratio between the backward voltagewave (toward the source) and the forward voltage wave (away from thesource), to be ρ_(s) at the source output, and to be ρ_(L) at the load,where${\rho_{s} = \frac{Z_{s} - Z_{0}}{Z_{s} + Z_{0}}},{\rho_{L} = {\frac{Z_{L} - Z_{0}}{Z_{L} + Z_{0}}.}}$

According to the wave propagation theory, the voltage at the output ofthe source, denoted as V₀, can be represented by a combination of anincident wave and infinite number of multi-reflections caused byimpedance discontinuity: $\begin{matrix}{{Incident}\quad{wave}\text{:}} & {V_{0}^{(0)} = \frac{Z_{0}}{Z_{0} + Z_{s}}} \\{1^{st}\quad{reflection}\text{:}} & \begin{matrix}{{{{Forward}\quad{wave}\quad V_{0}^{{(1)} +}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 2}\gamma\quad L} \cdot \rho_{L} \cdot \rho_{s}}},} \\{{{{Backward}\quad{wave}\quad V_{0}^{{(1)} -}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 2}\gamma\quad L} \cdot \rho_{L}}},}\end{matrix} \\{2^{nd}\quad{reflection}\text{:}} & \begin{matrix}{{{{Forward}\quad{wave}\quad V_{0}^{{(2)} +}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 4}\gamma\quad L} \cdot \rho_{L}^{2} \cdot \rho_{s}^{2}}},} \\{{{Backward}\quad{wave}\quad V_{0}^{{(2)} -}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 4}\gamma\quad L} \cdot \rho_{L}^{2} \cdot \rho_{s}}}\end{matrix} \\{3^{rd}\quad{reflection}\text{:}} & \begin{matrix}{{{{Forward}\quad{wave}\quad V_{0}^{{(3)} +}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 6}\gamma\quad L} \cdot \rho_{L}^{3} \cdot \rho_{s}^{3}}},} \\{{{Backward}\quad{wave}\quad V_{0}^{{(3)} -}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 3}\gamma\quad L} \cdot \rho_{L}^{2} \cdot \rho_{s}}}\end{matrix} \\\vdots & \vdots \\{n^{th}\quad{reflection}\text{:}} & \begin{matrix}{{{{Forward}\quad{wave}\quad V_{0}^{{(n)} +}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 2}n\quad\gamma\quad L} \cdot \rho_{L}^{n} \cdot \rho_{s}^{n}}},} \\{{{Backward}\quad{wave}\quad V_{0}^{{(n)} -}} = {V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 2}n\quad\gamma\quad L} \cdot \rho_{L}^{n} \cdot {\rho_{s}^{n - 1}.}}}\end{matrix}\end{matrix}$

Therefore, V₀ can be expressed as: $\begin{matrix}\begin{matrix}{V_{0} = {{\sum\limits_{n = 0}^{\infty}V_{0}^{(n)}} = {V_{0}^{(0)} + {\sum\limits_{n = 1}^{\infty}\left\lbrack {V_{0}^{{(n)} +} + V_{0}^{{(n)} -}} \right\rbrack}}}} \\{= {V_{0}^{(0)} + {\sum\limits_{n = 1}^{\infty}{V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 2}n\quad\gamma\quad L} \cdot \rho_{L}^{n} \cdot {\rho_{s}^{n - 1}\left( {1 + \rho_{s}} \right)}}}}} \\{= {V_{s} \cdot \frac{Z_{0}}{Z_{0} + Z_{s}} \cdot {\frac{1 + {{\mathbb{e}}^{{- 2}\gamma\quad L} \cdot \rho_{L}}}{1 - {{\mathbb{e}}^{{- 2}\gamma\quad L} \cdot \rho_{L} \cdot \rho_{s}}}.}}}\end{matrix} & (1)\end{matrix}$

Likewise, the voltage at the input of the load, denoted as V_(L), canalso be represented by a combination of multi-reflections: 1st Forwardwave V_(L) ⁽¹⁾⁺ = V₀ ⁽⁰⁾ · e^(−γL), reflection: Backward wave V_(L) ⁽¹⁾⁻= V₀ ⁽⁰⁾ · e^(−γL) · ρ_(L), 2nd Forward wave V_(L) ⁽²⁾⁺ = V₀ ⁽⁰⁾ ·e^(−3γL) · ρ_(L) · ρ_(S), reflection: Backward wave V_(L) ⁽²⁾⁻ = V₀ ⁽⁰⁾·e^(−3γL) · ρ_(L) ² · ρ_(S), 3rd Forward wave V_(L) ⁽³⁾⁺ = V₀ ⁽⁰⁾ ·e^(−5γL) · ρ_(L) ² · ρ_(S) ², reflection: Backward wave V_(L) ⁽³⁾⁻ = V₀⁽⁰⁾ · e^(−5γL) · ρ_(L) ³ · ρ_(S) ², . . . . . . . . . . . . . . . . . .n^(th) Forward wave V_(L) ^((n)+) = V₀ ⁽⁰⁾ · e^(−2(n−1)γL) · ρ_(L)^(n−1) · ρ_(S) ^(n−1), reflection: Backward wave V_(L) ^((n)−) = V₀ ⁽⁰⁾· e^(−2(n−1)γL) · ρ_(L) ^(n) · ρ_(S) ^(n−1).Therefore, V_(L) can be expressed as: $\begin{matrix}\begin{matrix}{V_{L} = {{\sum\limits_{n = 1}^{\infty}V_{L}^{(n)}} = {\sum\limits_{n = 1}^{\infty}\left\lbrack {V_{L}^{{(n)} +} + V_{L}^{{(n)} -}} \right\rbrack}}} \\{= {\sum\limits_{n = 1}^{\infty}{V_{0}^{(0)} \cdot {\mathbb{e}}^{{- {({{2n} - 1})}}\gamma\quad L} \cdot \rho_{L}^{n - 1} \cdot \left( {1 + \rho_{L}} \right) \cdot \rho_{s}^{n - 1}}}} \\{= {V_{s} \cdot \frac{Z_{0}}{Z_{0} + Z_{s}} \cdot {\frac{\left( {1 + \rho_{L}} \right){\mathbb{e}}^{{- \gamma}\quad L}}{1 - {{\mathbb{e}}^{{- 2}\gamma\quad L} \cdot \rho_{L} \cdot \rho_{s}}}.}}}\end{matrix} & (2)\end{matrix}$

Both a TDR measurement system and a DSL application can be representedby the equivalent circuitry shown in FIG. 1. In the TDR case, V_(s) isthe pulse sent down to the line, V₀ is the measured TDR echo. Theincident wave in V₀ is referred to as the near-end echo, the sum of themulti-reflections is referred to as the far-end echo. In a TDRmeasurement, the source impedance is usually the same as thecharacteristic impedance of the line, i.e. Z_(s)=Z₀, and the end of theline is usually open, i.e. Z_(L)=∞, thus ρ_(s)=0, ρ_(L)=1, and themeasured TDR echo can be written as: $\begin{matrix}{{V_{0} = {V_{s} \cdot \frac{Z_{0}}{Z_{0} + Z_{s}} \cdot \left( {1 + {\mathbb{e}}^{{- 2}\gamma\quad L}} \right)}},} & (3)\end{matrix}$which is a combination of the near-end echo and the backward wave in the1^(st) reflection.

In the DSL application case, V_(s) and Z_(s) represent the equivalentcircuitry of the modem at the central office (CO), and Z_(L) representsthe equivalent circuitry of the modem at the customer premise (CPE). Theobtainable data rate relates to the transfer function of the subscriberline, which is defined as: $\begin{matrix}{H = {\frac{V_{L}}{V_{0}}.}} & \quad\end{matrix}$

A modem is usually designed to have an impedance matching to the line,i.e. Z_(s)=Z₀, Z_(L)=Z₀, thus ρ_(s)=0, ρ_(L)=0, and V₀, V_(L), and H canbe written as: $\begin{matrix}{{V_{0} = {V_{s} \cdot \frac{Z_{0}}{Z_{0} + Z_{s}}}},{V_{L} = {V_{s} \cdot \frac{Z_{0}}{Z_{0} + Z_{s}} \cdot {\mathbb{e}}^{{- \gamma}\quad L}}},{H = {{\mathbb{e}}^{{- \gamma}\quad L}.}}} & (4)\end{matrix}$

Because the imaginary part of δ is a linear function of frequency, H haslinear phase, the data rate is mainly determined by the modular of thetransfer function.

Assume the transfer functions of two single-gauge straight lines to beH₁ and H₂. According to Eq. (4),H ₁ =e ^(−δ) ¹ ^(L) ¹ ,H ₂ =e ^(−δ) ² ^(L) ² ,where δ₁ and L₁ are the propagation constant and length of Line 1,respectively, and δ₂ and L₂ are the propagation constant and length ofLine 2, respectively. These two lines will have the same data rate if:real(δ₁)·L ₁=real(δ₂)·L ₂,  (5)where real(·) is an operation to obtain a variable's real part.

Assume the TDR echoes of these two lines to be V₀₁ and V₀₂. According toEq. (3),${V_{01} = {V_{s} \cdot \frac{Z_{01}}{Z_{01} + Z_{s}} \cdot \left( {1 + {\mathbb{e}}^{{- 2}\gamma_{1}L_{1}}} \right)}},{V_{02} = {V_{s} \cdot \frac{Z_{02}}{Z_{02} + Z_{s}} \cdot \left( {1 + {\mathbb{e}}^{{- 2}\gamma_{2}L_{2}}} \right)}},$where Z₀₁ and Z₀₂ are the characteristic impedance of Line 1 and Line 2.Ignoring the difference in characteristic impedance between these twolines, i.e. Z₀₁≈Z₀₂=Z₀, these two lines have similar near-end echoes,then according to Eq. (5), when these two lines have the same data rate,the following equation holds true: $\begin{matrix}{{{{V_{s}\frac{Z_{0}}{Z_{0} + Z_{s}}}} \cdot {\mathbb{e}}^{{{- 2} \cdot {{real}{(\gamma_{1})}}}L_{1}}} = {{{V_{s}\frac{Z_{0}}{Z_{0} + Z_{s}}}} \cdot {{\mathbb{e}}^{{{- 2} \cdot {{real}{(\gamma_{2})}}}L_{2}}.}}} & (6)\end{matrix}$

The left-hand side of Eq. (6) is the amplitude of the far-end TDR echoof Line 1; the right hand side is that of Line 2. Eq. (6) indicates thatthe far-end TDR echoes from two single-gauge straight lines, which havethe same data rate, and have the same amplitude. Although this deductionis derived for certain values of Z_(s) and Z_(L), the conclusion isapplicable for any Z_(s) and Z_(L).

An exemplary embodiment of the present invention is developed based onthis deduction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic representation of a transmission linesystem with a single-section straight loop;

FIG. 2 illustrates the exemplary spectrum of the TDR pulse usedaccording to an exemplary embodiment of this invention;

FIG. 3 illustrates exemplary spectra of the far-end echoes from 26AWGstraight loops with various lengths according to this invention;

FIG. 4 a illustrates a data rate comparison between equivalent-data-rateloops for the US data rate according to this invention;

FIG. 4 b illustrates a data rate comparison between equivalent-data-rateloops for the DS data rate according to this invention;

FIG. 5 a illustrates the far-end echo comparison between 24AWG and 26AWGequivalent-TDR-echo loops where the 26AWG equivalent loop length=5 kft.according to this invention;

FIG. 5 b illustrates the far-end echo comparison between 24AWG and 26AWGequivalent-TDR-echo loops where the 26AWG equivalent loop length=10 kft.according to this invention;

FIG. 6 illustrates schematically a representation of a transmission linesystem with a 2-section straight loop;

FIGS. 7 a and 7 b are a far-end echo comparison between mixed-gaugeloops and 26AWG equivalent loops according to this invention;

FIGS. 8 a and 8 b illustrate a data rate comparison between 2-sectionmixed-gauge loops and their 26AWG equivalent-data-rate loops for the USdata rate and DS data rate, respectively, according to this invention;

FIGS. 9 a and 9 b illustrate the data rate comparison between26AWG+24AWG loops and 24AWG+26AWG loops for the US data rate and the DSdate rate, respectively, according to this invention;

FIG. 10 illustrates a straight loop with mixed gauges according to thisinvention;

FIG. 11 illustrates an exemplary channel capacity estimator 100according to this invention;

FIGS. 12 a and 12 b illustrate the loop length estimation results, withFIG. 12 a showing a comparison between the actual and the estimatedlengths, and FIG. 12 b showing the distribution of the estimation erroraccording to this invention;

FIGS. 13 a and 13 b illustrate the US data rate estimation results, withFIG. 13 a showing a comparison between the actual and the estimated USdate rates, and FIG. 13 b showing the distribution of the estimationerror according to this invention;

FIGS. 14 a and 14 b illustrate the DS data rate estimation results, withFIG. 14 a showing a comparison between the actual and the estimated DSdate rates, and FIG. 14 b showing a distribution of the estimation erroraccording to this invention; and

FIG. 15 is a flowchart illustrating an exemplary operational flowaccording to this invention.

DETAILED DESCRIPTION

The exemplary embodiments of this invention will be described inrelation to acquiring, forwarding, if appropriate, and analyzingdiagnostic information in a communications environment. However, itshould be appreciated, that in general, the systems and methods of thisinvention would work equally well for any type of communication systemin any environment.

The exemplary systems and methods of this invention will be described inrelation to DSL modems and associated communication hardware, softwareand communication channels. However, to avoid unnecessarily obscuringthe present invention, the following description omits well-knownstructures and devices that may be shown in block diagram form orotherwise summarized.

For purposes of explanation, numerous details are set forth in order toprovide a thorough understanding of the present invention, it should beappreciated however that the present invention may be practiced in avariety of ways beyond the specific details set forth herein. Forexample, the systems and methods of this invention can generally beapplied to any type of communication system within any environment andfor the detection of a data rate in any digital communicationsenvironment.

Furthermore, while the exemplary embodiments illustrated herein show thevarious components of the system collocated, it is to be appreciatedthat the various components of the system can be located at distantportions of a distributed network, such as a telecommunications networkand/or the Internet, or within a dedicated secure, unsecured and/orencrypted system. Thus, it should be appreciated that the components ofthe system can be combined into one or more devices, such as a modem, orcollocated on a particular node of a distributed network, such as atelecommunications network. As will be appreciated from the followingdescription, and for reasons of computational efficiency, the componentsof the system can be arranged at any location within a distributednetwork without affecting the operation of the system. For example, thevarious components can be located in a Central Office (CO or ATU-C)modem, a Customer Premises Modem (CPE or ATU-R), or some combinationthereof. Similarly, the functionality of the system could be distributedbetween the modem and an associated computing device.

Furthermore, it should be appreciated that the various links, includingcommunications line 20, connecting the elements can be wired or wirelesslinks, or any combination thereof, or any other known or later developedelement(s) that is capable of supplying and/or communicating data to andfrom the connected elements. The term module as used herein can refer toany known or later developed hardware, software or combination ofhardware and software that is capable of performing the functionalityassociated with an element.

An exemplary embodiment of the present invention focuses on estimatingdata rates for asymmetric DSL (ADSL) service. However, and in general itis to be appreciated that this methodology can be applied to estimatedata dates for any digital communications line.

ADSL has an upstream (US) band, within which data is transmitted fromthe CPE to the CO, from Tone 6 to Tone 31, and a downstream (DS) band,within which data is transmitted from the CO to the CPE, from Tone 32 toTone 255. The tone interval can be, for example, 4312.5 Hz, with the ithtone corresponding to frequency (ƒ) according to ƒ_(i)=i×4312.5 (Hz).The TDR echo is measured by an ADSL CO modem within one frame, and isaveraged over 10,000 frames. Each frame has 512 time samples with thesampling rate being 2208 kHz. All subscriber lines are equivalent to asingle-gauge 26AWG straight loop.

For a straight loop with a single gauge, Gauge x, let the propagationconstant be δ_(x), the physical length be L_(x), then the equivalentequation given in Eq. (5) can be rewritten as:real(δ_(x))·L _(x)=real(δ₂₆)·L ₂₆,  (7)where δ₂₆ and L₂₆ is the propagation constant and loop length of thecorresponding 26AWG equivalent loop, respectively. Let the equivalentloop length ratio between Gauge x and 26AWG be α_(x), such thatL_(x)=α_(x)·L₂₆, then Eq. (7) becomes:real(δ_(x))·α_(x)=real(δ₂₆).  (8)

Because the propagation constant varies across frequency, a fixed ratioacross frequency has to be computed in a least square sense over acertain frequency band: $\begin{matrix}{{{a_{x}\left( {m,n} \right)} = \frac{\sum\limits_{i = m}^{n}{{{real}\left\lbrack {\gamma_{x}\left( f_{i} \right)} \right\rbrack} \cdot {{real}\left\lbrack {\gamma_{26x}\left( f_{i} \right)} \right\rbrack}}}{\sum\limits_{i = m}^{n}\left\{ {{real}\left\lbrack {\gamma_{x}\left( f_{i} \right)} \right\rbrack} \right\}^{2}}},} & (9)\end{matrix}$where ƒ_(i) is the frequency of the ith tone, and m and n determine thefrequency band under consideration. The equivalent ratio changes with mand n.

Because a subscriber line provides more attenuation on higher frequencycomponents than on lower frequency components, the measured TDR echo isdominated by low frequency components. The spectrum of the pulse alsoinfluences the frequency band of the measured TDR echo. FIG. 2 shows thespectrum of the TDR pulse used in this invention. FIG. 3 shows thespectra of the far-end echoes from 26AWG straight loops with variouslengths. Eighteen curves are plotted in each plot. Each curvecorresponds to a 26AWG loop with a certain length. The loop lengthvaries from 1 kft to 18 kft in 1 kft step. It can be seen that thefar-end echo is dominated by low frequency components, and more than 95%of the energy is distributed below Tone 50 (≅220 kHz). Since there isnot much energy below Tone 6, the TDR band is set in this exemplaryembodiment from Tone 6 to 50, however, the TDR band can be varied asappropriate.

As discussed above, the US band of an ADSL application is from Tone 6 toTone 31, the DS band is from Tone 32 to Tone 255, so the equivalentratio for the US case is different from the DS case. Consider thedifference in frequency band among the US, DS, and TDR case, define:

-   -   α_(x(eq) _(—) _(us))=equivalent loop length ratio corresponding        to the same US data rate,    -   α_(x(eq) _(—) _(ds))=equivalent loop length ratio corresponding        to the same DS data rate, and    -   α_(x(eq) _(—) _(tdr))=equivalent loop length ratio corresponding        to the same far-end echo (shape and amplitude only),        then the equation for determining each ratio using Eq. (9) is        α_(x(eq) _(—) _(us))=α_(x)(m=6, n=31),        α_(x(eq) _(—) _(ds))=α_(x)(m=32, n=255),        α_(x(eq) _(—) _(tdr))=α_(x)(m=6, n=50).

Table 1 shows the equivalent ratios for both American loops (AWG) andEuropean loops (metric). All ratios are determined using the wireprimary parameters, characteristic impedance Z₀ and propagation constantδ, published in ITU G.996.1. TABLE 1 Equivalent coefficients Equivalent-Equivalent- Equivalent- TDR-echo Velocity Time-shift US-Rate RatioDS-rate Ratio Ratio Coefficient Coefficient Gauge x a_(x(eq) _(—) _(us))a_(x(eq) _(—) _(ds)) a_(x(eq) _(—) _(tdr)) V_(x) (sample/kft) τ_(x)(ft/sample) 0.32 mm  0.8 0.8 0.8 6.3 ANY 0.4 mm 1.0 1.0 1.0 6.9 ANY 0.5mm 1.5 1.3 1.5 7.5 30 0.63 mm  2.2 1.6 2.0 6.9 40 0.9 mm 3.3 2.2 3.0 6.530 19AWG 3.2 2.3 2.8 6.9 20 22AWG 2.0 1.6 1.9 7.1 30 24AWG 1.4 1.27 1.47.1 40 26AWG 1.0 1.0 1.0 7.0 ANY

FIG. 4 shows the data rate comparison between 24AWG and 26AWGequivalent-data-rate loops. More specifically, FIG. 4 a illustrates thedata rate comparison between equivalent US data rate loops and FIG. 4 billustrates data rate comparison between equivalent DS data rate loops.According to Table 1, the equivalent-US-rate ratio is 1.4; theequivalent-DS-rate ratio is 1.27. FIG. 4(a) shows the US data rates of24AWG loops (length=L) versus that of 26AWG equivalent-US-rate loops(length=L/1.4). FIG. 4(b) shows the DS data rates of 24AWG loops(length=L) versus that of 26AWG equivalent-DS-rate loops(length=L/1.27). It can be seen that the equivalent loops do have verysimilar data rate. The averaged data rate difference between equivalentloops is about 30 kbps for the US case, and 160 kbps for the DS case.

FIG. 5 illustrates the far-end echo comparison between 24AWG and 26AWGequivalent-TDR-echo loops. According to Table 1, the equivalent-TDR-echoratio is 1.4. FIG. 5 a shows the comparison between a 26AWG 5 kft loopand a 24AWG 7 kft loop (5*1.4=7). FIG. 5 b shows the comparison betweena 26AWG 10 kft loop and a 24AWG 14 kft loop (10*1.4=14). It can be seenthat between the equivalent loops, the amplitude and the shape of thefar-end echoes are very similar; while the time delays are different—the24AWG loop has a longer delay than the 26AWG loop.

The equivalent ratios given in Table 1 are computed under the assumptionthat the difference in characteristic impedance Z₀ can be ignored. Thecomparisons shown in FIG. 4 and in FIG. 5 indicate this approximation isreasonable.

Due to the existence of gauge changes within a mixed-gauge loop, themixed-gauge case is more complicated than the single gauge case. Anexemplary transmission line system with a two-section mixed-gauge loopis schematically represented in FIG. 6. It is similar to that shown inFIG. 1. The only difference is the line has two sections instead of onesection.

Let the characteristic impedance, propagation constant, and loop lengthof the first section be Z₀₁, δ₁ and L₁, and that of the second sectionbe Z₀₂, δ₂ and L₂. The gauge change point is denoted as A, and thereflection coefficient at A as ρ_(A), where:$\rho_{A} = {\frac{Z_{02} - Z_{01}}{Z_{02} + Z_{01}}.}$

According to the transmission line theory, the wave propagation withinthis two-section loop can be represented as follows:Incident wave: $V_{0}^{(0)} = {\frac{Z_{01}}{Z_{s} + Z_{01}}{V_{s}.}}$1^(st) trip, wave at A:Forward wave V _(A12) ⁽¹⁾⁺ =V ₀ ⁽⁰⁾ ·e ^(−δ) ¹ ^(L) ¹Backward wave V _(A12) ⁽¹⁾⁻ =V ₀ ⁽⁰⁾ ·e ^(−δ) ¹ ^(L) ¹ ·ρ_(A)1^(st) trip, incident from Section 1 to Section 2:V _(A12) ⁽¹⁾ =V _(A12) ⁽¹⁾⁺ +V _(A12) ⁽¹⁾⁻ =V ₀ ⁽⁰⁾ ·e ^(−δ) ¹ ^(L) ¹·(1+ρ_(A))1^(st) trip, return from the end of Section 2 to A:Forward wave V _(A21) ⁽¹⁾⁺ =V _(A12) ⁽¹⁾ ·e ⁻² ^(δ2) ^(L) ²·(−ρ_(A))·ρ_(L)Backward wave V _(A21) ⁽¹⁾⁻ =V _(A12) ⁽¹⁾ ·e ⁻² ^(δ2) ^(L) ² ·ρ_(L)1^(st) trip, incident from Section 2 to Section 1:V _(A21) ⁽¹⁾ =V _(A21) ⁽¹⁾⁺ +V _(A21) ⁽¹⁾⁻1^(st) reflection at the source output: $\begin{matrix}\begin{matrix}{V_{0}^{(1)} = {\left\lbrack {{V_{A\quad 12}^{{(1)} -} \cdot {\mathbb{e}}^{{- \gamma_{1}}L_{1}}} + {V_{A\quad 21}^{(1)} \cdot {\mathbb{e}}^{{- \gamma_{1}}L_{1}}}} \right\rbrack \cdot \left( {1 + \rho_{s}} \right)}} \\{= {\left\lbrack {{V_{A\quad 12}^{{(1)} -} \cdot {\mathbb{e}}^{{- \gamma_{1}}L_{1}}} + {\left( {V_{A\quad 21}^{{(1)} +} + V_{A\quad 21}^{{(1)} -}} \right) \cdot {\mathbb{e}}^{{- \gamma_{1}}L_{1}}}} \right\rbrack \cdot \left( {1 + \rho_{s}} \right)}} \\{= {\left\lbrack {{V_{0}^{(0)} \cdot {\mathbb{e}}^{{- 2}\gamma_{1}L_{1}} \cdot \rho_{A}} + {V_{0}^{(0)} \cdot {\mathbb{e}}^{{{- 2}\gamma_{1}L_{1}} - {2\gamma_{2}L_{2}}} \cdot \left( {1 - \rho_{A}^{2}} \right) \cdot \rho_{L}}} \right\rbrack \cdot \left( {1 + \rho_{s}} \right)}} \\{= {{V_{s}{\frac{Z_{01}}{Z_{01} + Z_{s}} \cdot {\mathbb{e}}^{{- 2}\gamma_{1}L_{1}} \cdot \rho_{A} \cdot \left( {1 + \rho_{s}} \right)}} +}} \\{V_{s}{\frac{Z_{01}}{Z_{01} + Z_{s}} \cdot {\mathbb{e}}^{{{- 2}\gamma_{1}L_{1}} - {2\gamma_{2}L_{2}}} \cdot \left( {1 - \rho_{A}^{2}} \right) \cdot \rho_{L} \cdot \left( {1 + \rho_{s}} \right)}}\end{matrix} & (10)\end{matrix}$

When each section is not too short (e.g., L₁, L₂>1000 ft), higher orderreflections can be ignored, thus the 1^(st) order reflection given byEq. (10) is a reasonable approximation of the overall far-end echo. Eq,10 shows that the far-end echo includes two dominant reflections, one isfrom the gauge change (the first term in Eq. (10)), the other is fromthe end of the line (the second term in Eq. (10)). Because thereflection coefficient at the gauge change, ρ_(A), is usually verysmall, ρ_(A) ² is even smaller, the reflection from the end of the linecan be simplified to: $\begin{matrix}{V_{s} \cdot \frac{Z_{01}}{Z_{01} + Z_{s}} \cdot {\mathbb{e}}^{{{- 2}\gamma_{1}L_{1}} - {2\gamma_{2}L_{2}}} \cdot \rho_{L} \cdot {\left( {1 + \rho_{s}} \right).}} & (11)\end{matrix}$

Assume the equivalent-TDR ratio of a 26AWG loop to be α_(1(eq) _(—)_(tdr)) for Section 1, and α_(2(eq) _(—) _(tdr)) for Section 2. Eq. (11)indicates that if Z₀₁ is similar to the characteristic impedance of a26AWG loop, the reflection from the end of the mixed-gauge loop has asimilar shape and amplitude as the far-end echo from a 26AWG loop withlengthL _(eq) _(—) _(tdr) =L ₁/α_(1(eq) _(—) _(tdr)) +L ₂/α_(2(eq) _(—)_(tdr)).

FIG. 7 shows far-end echo comparisons between a mixed-gauge loop and its26AWG equivalent-TDR-echo loop. More specifically, FIG. 7 a shows thecomparison between a mixed-gauge loop, which has a first section of 3kft 26AWG and a second section of 3 kft 24AWG, and a 26AWG straight loopwith a length of 5.1 kft (3+3/1.4=5.1). FIG. 7 b shows the comparisonbetween a mixed-gauge loop, which has a first section of 2 kft 24AWG anda second section of 5 kft 26AWG, and a 26AWG straight loop with a lengthof 6.4 kft (2/1.4+5=6.4). FIG. 7(a) suggests that in the mixed-gaugecase, although part of the far-end echo is the return from the gaugechange, the return from the end of the loop is very similar to thefar-end echo from the equivalent straight loop. The sign of the returnfrom the gauge change is the inverse of the return from the end of theloop. This is consistent with the fact that the gauge change is from26AWG to 24AWG. Because the characteristic impedance of a 24AWG loop issmaller than that of a 26AWG loop, the reflection coefficient at thegauge change is negative, which results in a negative return.

Similar to FIG. 7 a, FIG. 7 b also suggests that in the mixed-gaugecase, although part of the far-end echo is the return from the gaugechange, the return from the end of the loop is very similar to thefar-end echo from the equivalent straight loop. However, now the gaugechange is from 24AWG to 26AWG, the reflection coefficient at the gaugechange is positive, so the return from the gauge change is somewhatsimilar to the return from the end of the loop. Therefore, it isexpected that the return from the gauge change may have more influenceon 24AWG+26AWG mixed-gauge case than on 26AWG+24AWG mixed-gauge case.

Assume Z_(s)=Z₀₁, Z_(L)=Z₀₂, the voltage at the load input, V_(L), is:V _(L) =V _(A12) ⁽¹⁾ ·e ^(−δ) ² ^(L) ² =V ₀ ⁽⁰⁾ ·e ^(−δ) ¹ ^(L) ¹ ^(−δ)² ^(L) ² ·(1+ρ_(A)),therefore, the transfer function of the mixed-gauge line is:$\begin{matrix}{H = {\frac{V_{L}}{V_{0}} = {{\mathbb{e}}^{{{- \gamma_{1}}L_{1}} - {\gamma_{2}L_{2}}} \cdot {\left( {1 + \rho_{A}} \right).}}}} & (12)\end{matrix}$

As mentioned before, the reflection coefficient at the gauge change,ρ_(A), is usually very small, thus the transfer function can besimplified to:H≈e ^(−δ) ¹ ^(L) ¹ ^(−δ) ² ^(L) ² .  (13)

Assume the equivalent US and DS ratios to a 26AWG loops to be α_(1(eq)_(—) _(us)) and α_(1(eq) _(—) _(ds)) for Section 1, and α_(2(eq) _(—)_(us)) and α_(2(eq) _(—) _(ds)) for Section 2. Eq. 13 indicates that the2-section loop has the same data rate as a 26AWG straight loop withlength:L _(eq) _(—) _(us) =L ₁/α_(1(eq) _(—) _(us)) +L _(2/α) _(2(eq) _(—)_(us)),and has the same DS data rate as a 26AWG straight loop with length:L _(eq) _(—ds) =L ₁/α_(1(eq) _(—) _(ds)) +L ₂/α_(2(eq) _(—) _(ds)).

FIG. 8 shows data rate comparison between 2-section mixed-gauge loopsand their 26AWG equivalent-data-rate loops. The first section of eachloop is 26AWG and the second section is 24AWG. Each section varies from1 kft to 9 kft in 500 ft step. It can be seen that the approximationgiven in Eq. (13) is reasonable.

FIG. 9 illustrates the data rate comparison between 2-section loops withdifferent gauge change order: one case is from 26AWG to 24AWG; the othercase is from 24AWG to 26AWG. It can be seen that the data rates of thesetwo cases are very similar. According to Eq. (12), the transfer functionof the 26AWG+24AWG case be written as:H _(26AWG+24AWG) =e ^(−δ) ²⁶ ^(L) ²⁶ ^(−δ) ²⁴ ^(L) ²⁴ ·(1+ρ_(A)),and the 24AWG+26AWG case be written as:H _(24AWG+26AWG) =e ^(−δ) ²⁴ ^(L) ²⁴ ^(−δ) ²⁶ ^(L) ²⁶ ·(1−ρ_(A)),thus the difference between these two cases is the sign of thereflection coefficient. The similarity in data rates between these twocases indicates the reflection at the gauge change has no significantinfluence on the data rates. Therefore, Eq. (13) is a reasonableapproximation of the transfer function of a 2-section loop.

Although Eq. (11) and Eq. (13) are derived for 2-section loops, theyhold true for multi-section loops as well. For a loop with n sections,assume the physical length, equivalent US ratio, equivalent DS ratio,and equivalent TDR ratio for the ith section (i=1−n) to be L_(i),α_(i(eq) _(—) _(us)), α_(i(eq) _(—) _(ds)), and α_(i(eq) _(—) _(tdr)),respectively. Let the 26AWG equivalent US length, equivalent DS length,and equivalent TDR length be L_(eq) _(—) _(us), L_(eq) _(—) _(ds), andL_(eq) _(—) _(tdr), respectively, then:${L_{eq\_ us} = {\sum\limits_{i = 1}^{n}{L_{i}/a_{i{({eq\_ us})}}}}},{L_{eq\_ ds} = {\sum\limits_{i = 1}^{n}{L_{i}/a_{i{({eq\_ ds})}}}}},{L_{eq\_ tdr} = {\sum\limits_{i = 1}^{n}{L_{i}/{a_{i{({eq\_ tdr})}}.}}}}$

As mentioned above, the ultimate goal of the equivalent loop estimationis to predict the data rate for a given loop. The equivalent lengthestimated from the measured TDR echo is the equivalent TDR length.According to Table 1, the equivalent TDR ratio and the equivalent datarate ratio, especial in the DS case, are different, thus the data ratepredicted using the equivalent TDR length would be inaccurate. In anexemplary embodiment of the present invention, the equivalent-data-ratelength is derived from the estimated equivalent TDR length and the timedelay between the measured far-end echo and the equivalent far-end echo.

The time delay of a far-end echo is determined by the physical length ofthe loop and the propagation velocity of the traveling wave. Based onthe transmission line theory, the time delay can be represented as:${{Delay} = \frac{2L}{V_{p}}},$where L is the physical length of the loop, and V_(p) is the propagationvelocity. Since a far-end echo is a round trip return, the numerator isdouble loop length. The propagation velocity of a transmission linerelates to the imaginary part of the propagation constant δ,${V_{p} = \frac{\omega}{{imag}\quad(\gamma)}},$where ω is the radian frequency (ω=2πƒ), and imag(δ) is the imaginarypart of δ. Because a subscriber line usually has a propagation constantwhose imaginary part is a straight line across frequency, thepropagation velocity is a constant across frequency. Thus, thepropagation velocity of Gauge x, denoted as V_(x), can be computed fromthe propagation constant as in the following $\begin{matrix}{{V_{x} = \frac{2{\pi \cdot \Delta}\quad f}{\frac{1}{n - m}\left\{ {{{imag}\left\lbrack {\gamma_{x}\left( f_{n} \right)} \right\rbrack} - {{imag}\left\lbrack {\gamma_{x}\left( f_{m} \right)} \right\rbrack}} \right\}}},} & (14)\end{matrix}$where ƒ_(i) is the frequency of the ith tone, δ_(x) is the propagationconstant of Gauge x, Δƒ is the tone interval, which in the ADSL case is4312.5 Hz, and m and n correspond to the frequency range of the TDRecho. In this specific case, m=6, n=50. The unit for V_(x) is “m/s”.

The propagation velocity can be expressed in terms of number of samplesper kft. For Gauge x, define number of samples per kft as velocitycoefficient λ_(x), then:${\lambda_{x} = {\frac{2 \times 1000\quad({ft})}{3.2808\quad\left( {{ft}\text{/}m} \right)} \cdot \frac{f_{s}}{V_{x}}}},$where ƒ_(s) is the sampling rate of the TDR measurement system. The unitfor λ_(x) is “Time Sample/kft”. The velocity coefficient of AWG loopsand metric loops are listed in Table 1 for ƒ_(s)=2208 kHz. It can beseen that a 24AWG loop has almost the same velocity coefficient as a26AWG loop, about 7 samples/kft. Consider the equivalent TDR ratiobetween a 26AWG loop and a 24AWG loop is 1.4, the delay difference, orthe time shift, between a 24AWG loop (length=L) and its 26AWG equivalentloop (length=L/1.4) is L×7−L/1.4×7=2×L, where L is in kft. For thefar-end echoes shown in FIG. 5 and FIG. 7, the theoretical time shiftsbetween the measured far-end echo and its TDR-equivalent loop are:

-   -   FIG. 5(a): 24AWG length=7 kft, time shift=14 samples;    -   FIG. 5(b): 24AWG length=10 kft, time shift=28 samples;    -   FIG. 7(a): 26AWG length=3 kft, 24AWG length=3 kft, time shift=6        samples;    -   FIG. 7(b): 24AWG length=2 kft, 26AWG length=5 kft, time shift=4        samples.

The time shifts given above are consistent with the plots given in FIGS.5 and 7. This indicates the time shift contains the information aboutthe physical length of a given loop.

For a straight loop with a single gauge, Gauge x, if its physical lengthis L_(x), then the equivalent-TDR length L_(eq) _(—)_(tdr)=L_(x)/α_(x(eq) _(—) _(tdr)). Let the velocity coefficient ofGauge x be λ_(x), and that of 26AWG be λ₀, then the time shift betweenthe measured echo and the equivalent echo, denoted as s, is:s=L _(x)·λ_(x) −L _(eq) _(—) _(tdr)·λ₀,where the unit of s is number of samples. The physical length, L_(x),can be rewritten as: $\begin{matrix}{L_{x} = {\frac{s}{\lambda_{x} - {\lambda_{0}/a_{x{({eq\_ tdr})}}}}.}} & (15)\end{matrix}$

Eq. (15) shows that once Gauge x is known, the physical length of astraight loop, L_(x), can be obtained directly from the time shift s.

For a straight loop mixed with 26AWG and Gauge x, as illustrated in FIG.10, assume the length of the 26AWG section to be Lo and that of Gauge xto be L_(x). If we know λ₀, λ_(x), α_(x(eq) _(—) _(tdr)), α_(x(eq) _(—)_(ds)), the equivalent-TDR length L_(eq) _(—) _(tdr), and the time shifts, then the equivalent-DS-rate length, denoted as L_(eq) _(—) _(ds), canbe obtained by solving the following equations: $\left\{ {\begin{matrix}{L_{eq\_ tdr} = {L_{0} + {L_{x}/a_{x{({eq\_ tdr})}}}}} \\{L_{eq\_ ds} = {L_{0} + {L_{x}/a_{x{({eq\_ ds})}}}}} \\{L_{x} = {s/\left( {\lambda_{x} - {\lambda_{0}/a_{x{({eq\_ tdr})}}}} \right)}}\end{matrix}.} \right.$

The solution is: $\begin{matrix}{{L_{eq\_ ds} = {L_{eq\_ tdr} + s}}{\cdot \frac{1}{\lambda_{x} - {\lambda_{0}/a_{x{({eq\_ tdr})}}}} \cdot {\left\lbrack {\frac{1}{a_{x{({eq\_ ds})}}} - \frac{1}{a_{x{({eq\_ tdr})}}}} \right\rbrack.}}} & (16)\end{matrix}$

Define the time-shift coefficient for Gauge x be τ_(x), i.e.:${\tau_{x} = {\frac{1}{\lambda_{x} - {\lambda_{0}/a_{x{({eq\_ tdr})}}}} \cdot \left\lbrack {\frac{1}{a_{x{({eq\_ ds})}}} - \frac{1}{a_{x{({eq\_ tdr})}}}} \right\rbrack}},$then Eq. (16) can be written as:L _(eq) _(—) _(ds) =L _(eq) _(—) _(tdr) +s·τ _(x).  (17)

Eq. (17) shows that the equivalent-data-rate length, L_(eq) _(—) _(ds)can be determined based on the equivalent-TDR-echo length, L_(eq) _(—)_(tdr), the time shift s, and the time shift coefficient τ_(x). Table 1lists the time shift coefficients of both AWG wires and metric wires.Because for 0.4 mm and 26AWG wires, the time shift is 0 for any looplength, in other words, the equivalent-data length, theequivalent-TDR-echo length and the physical length are the same forthese wires, the time-shift coefficient for these two gauges can be anyvalue. Eq. (17) indicates that if the time shift coefficient, τ_(x), isa constant across all gauges, the relationship given by Eq. (17) wouldbe independent of Gauge x. However, Table 1 shows the time-shiftcoefficients are not identical across gauge. Since the most populargauges used in the field are 24AWG and 26AWG in North American, and 0.4mm, 0.5 mm, and 0.63 mm in Europe, we average the time shift coefficientacross 24AWG, 0.5 mm and 0.63 mm, the rounded average is τ_(mean)≈40.

Because the equivalent-US-rate ratio is very similar to theequivalent-TDR ratio, no correction is made for US rate prediction.

As discussed, the goal of the equivalent estimation method is to predictthe data rate for a given subscriber line based on a TDR measurement.The input of the method is a measured TDR echo, the output is thepredicted DS and US data rates. The intermediate steps include theequivalent TDR length estimation and the length correction for data rateprediction. In order to predict the data rate correctly, this exemplarymethod needs to know the data rate versus loop length curve of 26AWGstraight loops. The detailed procedure is discussed below in relation toFIGS. 11 and 12.

FIG. 11 illustrates an exemplary channel capacity estimator 100according to this invention. The estimator 100 comprises a TDRmeasurement module 110, a theoretical TDR echo determination module, anequivalent TDR length estimation module 130, an optimizer module 140, amemory 150, a controller 160, a correction module 170 and an US and DSdata rate prediction module 180, all interconnected by link 5. Theestimator 100 is connected to a line 20, which is in turn connected to amodem 200, such as a DSL modem.

In operation, the TDR measurement module 110 reads a previously measuredor determines the measured TDR echo, (echo_measured(i)), where i is thetime sample index. In the case of ADSL, one flame has 512 samples, thusi=0-511.

Next, the theoretical TDR echo determination module 120 determines thetheoretical TDR echoes for 26AWG straight loops with various looplengths.

Let the loop length of the nth loop be L_(n), n=1−N, where N is totalnumber of loops, the corresponding theoretical TDR echo beecho_model_(n)(i), then:${{{echo\_ model}_{n}(i)} = {{IFFT}\left\lbrack {\frac{Z_{0}/{\tanh\left( {\gamma\quad L_{n}} \right)}}{Z_{s} + {Z_{0}/{\tanh\left( {\gamma\quad L_{n}} \right)}}}V_{s}} \right\rbrack}},$where Z₀ and 67 are the characteristic impedance and propagationconstant of a 26AWG loop, Z_(s) and V_(s) are the output impedance andvoltage of the source.

Then, the equivalent TDR length estimation module 130 estimates theequivalent TDR length. This is achieved by:

-   -   (1) Finding the best time shift between the measured far-end        echo and the theoretical far-end echo of the nth loop by solving        the following optimization problem:        ${\min\limits_{m}{\sum\limits_{j = 0}^{{WN} - 1}\left\lbrack {{{echo\_ measured}\left( {j + m} \right)} - {{echo\_ model}_{n}(j)}} \right\rbrack^{2}}},$    -    where m is a variable representing the time shift, which varies        in a certain region with a one-sample step. The minimum error        across m is denoted as E(n), and the corresponding best shift as        S(n).    -   (2) Let n=n+1. If n≦N, go to (1); otherwise go to (3).    -   (3) ${{{Let}\quad n^{*}} = {\min\limits_{n}\quad{E(n)}}},$        then the equivalent TDR length, L_(eq) _(—) _(tdr), is:        L _(eq) _(—) _(tdr) =L _(n*),        and the corresponding time shift, denoted as s*, is:        s*=S(n*).

The correction module 170 then corrects the equivalent-TDR length fordata rate prediction.

According to the analysis given above, the equivalent-US-rate length andthe equivalent-DS-rate length relate to L_(eq) _(—) _(tdr) and s*.L _(eq) _(—) _(us) =L _(eq) _(—) _(tdr), andL _(eq) _(—) _(dr) =L _(eq) _(—) _(tdr) +s*·τ _(mean) =L _(eq) _(—)_(tdr) +s*·40(ft/sample).

The US and DS data rate prediction module 180 then predicts the US andDS data rates, which can be one or more of output and or displayed on adisplay device (not shown), by letting the US rate-length function for26AWG loops be Rate_(US)(E), and the DS rate-length function beRate_(DS)(L), then the US rate, denoted as US_Rate, and the DS rate,denoted as DS_Rate, are:US_Rate=Rate_(US)(L _(eq) _(—) _(us)), andDS_Rate=Rate_(DS)(L _(eq) _(—) _(ds)).

The present invention has been tested on several different CO modemsthat have TDR functionality. The results from one of the modems aregiven below. All of the loops tested are listed in Table 2. The totalnumber of loops is 1291. AU loops are straight loops with a singlesection or up to four sections. Both American wires and European wiresare tested. FIG. 12 shows the estimation results on equivalent-TDRlength, with FIG. 12 a showing the estimated length versus theoreticallength, which is calculated using Table 1, and FIG. 12 b showing thedistribution of the estimation error.

FIG. 13 shows the estimation results on US data rate, with FIG. 13 ashowing the estimated US rate versus the measured data rate, i.e. theactual data rate when connecting a CO-CPE modem pair using the givenloop, and FIG. 13 b showing the distribution of the error on US rateestimation.

FIG. 14 shows the estimation results on DS data rate, with FIG. 14 ashowing the estimated DS rate versus the measured data rate, i.e. theactual data rate when connecting a CO-CPE modem pair using the givenloop, and FIG. 14 b showing the distribution of the error on DS rateestimation. TABLE 2 A list of exemplary tested loops No. No. of ofsections Configuration Length loops 1-section 24AWG (L) L = 1 kft − 22kft/1 kft 22 26AWG (L) L = 1 kft − 18 kft/100 ft 171 0.4 mm (L) L = 200m − 3500 m/50 m 67 0.5 mm (L) L = 200 m − 5000 m/50 m 97 2-section 26AWG(L1) + 24AWG(L2) L1, L2 = 1 kft − 9 kft/500 ft 289 0.4 mm(L1) + 0.5mm(L2) L1, L2 = 200 m − 3000 m/200 m 225 ETSI #3 (L = length of 0.4 mm L= 50 m − 3000 m/50 m 60 section) 3-section 26awg(L1) + 24awg(L2) +26awg(L3) L1, L2, L3 = 1 kft − 9 kft/2 kft 90 L1 + L2 + L3 <= 18 kftETSI #6 (L = length of 0.4 mm L = 50 m − 3000 m/50 m 60 section) ETSI #7(L = length of 0.4 mm L = 50 m − 3000 m/50 m 60 section) 4-section26awg + 24awg + 26awg + 24awg The length of each section is 30 randomlychosen. The total physical length is less than 18 kft. ETSI #4 (L =length of 0.4 mm L = 50 m − 3000 m/50 m 60 section) ETSI #5 (L = lengthof 0.4 mm L = 50 m − 3000 m/50 m 60 section)

Exemplary FIGS. 12, 13 and 14 indicate that the equivalent-TDR lengthestimation error is less than 500 ft for 96% of the loops; that the USdata rate estimation error is less than 100 kbps for 99% of the loops,and that the DS data rate estimation error is less than 500 kbps for 97%of the loops.

FIG. 15 illustrates an exemplary method of predicting data ratesaccording to this invention. In particular, control begins in step S100and continues to step S200. In step S200, a measured TDR echo, isobtained. Next, in step S300, the theoretical TDR echo for 26AWGstraight loops with various loop lengths are determined and stored. Itis to be appreciated however that the gauge of the equivalent loop doesnot necessary have to be 26AWG, to the contrary, the gauge could be anygauge. The only requirement is the data rate of the selected gaugeshould be known. Furthermore, the described methodology is not onlyapplicable to single gauge straight loops, but also multi-section loopswith different gauges as well as loops with bridged taps.

Then, in step S400, the equivalent TDR length is estimated. As discussedabove, this is determined by:

-   -   (1) Finding the best time shift between the measured far-end        echo and the theoretical far-end echo of the nth loop by solving        the following optimization problem:        ${\min\limits_{m}{\sum\limits_{j = 0}^{{WN} - 1}\left\lbrack {{{echo\_ measured}\left( {j + m} \right)} - {{echo\_ model}_{n}(j)}} \right\rbrack^{2}}},$    -   (2) where m is a variable representing the time shift, which        varies in a certain region with a one-sample step. The minimum        error across m is denoted as E(n), and the corresponding best        shift as S(n).    -   (3) Let n=n+1. If n≦N, go to (1); otherwise go to (3).    -   (4) ${{{Let}\quad n^{*}} = {\min\limits_{n}\quad{E(n)}}},$        then the equivalent TDR length, L_(eq) _(—) _(tdr), is:        L _(eq) _(—) _(tdr) =L _(n*),    -   (5) and the corresponding time shift, denoted as s*, is:        s*=S(n*).        Control then continues to step S500.

In step S500, the equivalent-TDR length for data rate prediction iscorrected. According to the analysis given above, the equivalent-US-ratelength and the equivalent-DS-rate length relate to L_(eq) _(—) _(tdr)and s*:L_(eq) _(—) _(us)=L_(eq) _(—) _(tdr), andL _(eq) _(—) _(ds) =L _(eq) _(—) _(tdr) +s*·τ _(mean) =L _(eq) _(—)_(tdr) +s*·40(ft/sample).

The US and DS data rates are then predicted in steps S600 and S700,respectively, in accordance with the following, which can be one or moreof output and or displayed on a display device (not shown), by lettingthe US rate-length function for 26AWG loops be Rate_(US)(E), and the DSrate-length function be Rate_(DS)(E), then the US rate, denoted asUS_Rate, and the DS rate, denoted as DS_Rate, are:US_Rate=Rate_(US)(L _(eq) _(—) _(us)), andDS_Rate=Rate_(DS)(L _(eq) _(—) _(ds)).One or more of the US and DS data rate(s) are then output in step S800and control continues to step S900 where the control sequence ends.

The above-described system can be implemented on wired and/or wirelesstelecommunications devices, such a modem, a multicarrier modem, a DSLmodem, an ADSL modem, an XDSL modem, a VDSL modem, a linecard, testequipment, a multicarrier transceiver, a wired and/or wirelesswide/local area network system, a satellite communication system, amodem equipped with diagnostic capabilities, or the like, or on aseparate programmed general purpose computer having a communicationsdevice.

Additionally, the systems, methods and protocols of this invention canbe implemented on a special purpose computer, a programmedmicroprocessor or microcontroller and peripheral integrated circuitelement(s), an ASIC or other integrated circuit, a digital signalprocessor, a hard-wired electronic or logic circuit such as discreteelement circuit, a programmable logic device such as PLD, PLA, FPGA,PAL, modem, transmitter/receiver, or the like. In general, any devicecapable of implementing a state machine that is in turn capable ofimplementing the methodology illustrated herein can be used to implementthe various communication methods, protocols and techniques according tothis invention.

Furthermore, the disclosed methods may be readily implemented insoftware using object or object-oriented software developmentenvironments that provide portable source code that can be used on avariety of computer or workstation platforms. Alternatively, thedisclosed system may be implemented partially or fully in hardware usingstandard logic circuits or VLSI design. Whether software or hardware isused to implement the systems in accordance with this invention isdependent on the speed and/or efficiency requirements of the system, theparticular function, and the particular software or hardware systems ormicroprocessor or microcomputer systems being utilized. Thecommunication systems, methods and protocols illustrated herein howevercan be readily implemented in hardware and/or software using any knownor later developed systems or structures, devices and/or software bythose of ordinary skill in the applicable art from the functionaldescription provided herein and with a general basic knowledge of thecomputer and telecommunications arts.

Moreover, the disclosed methods may be readily implemented in software,that can be stored on a storage medium, executed on programmedgeneral-purpose computer, a special purpose computer, a microprocessor,or the like. In these instances, the systems and methods of thisinvention can be implemented as program embedded on personal computersuch as JAVA® or CGI script, as a resource residing on a server orcomputer workstation, as a routine embedded in a dedicated communicationsystem or system component, or the like. The system can also beimplemented by physically incorporating the system and/or method into asoftware and/or hardware system, such as the hardware and softwaresystems of a communications transceiver and operations support system.

It is therefore apparent that there has been provided, in accordancewith the present invention, systems and methods for estimating channeldata rate. While this invention has been described in conjunction with anumber of embodiments, it is evident that many alternatives,modifications and variations would be or are apparent to those ofordinary skill in the applicable arts. Accordingly, it is intended toembrace all such alternatives, modifications, equivalents and variationsthat are within the spirit and scope of this invention.

1. A method for channel capacity estimation comprising: obtaining a measured TDR echo; determining a theoretical TDR echo for a plurality of loop lengths; estimating the equivalent TDR length based on an optimization; updating the equivalent TDR length; and utilizing the updated TDR length to predict one or more of the upstream and downstream data rates.
 2. The method of claim 1, further comprising determining a time shift between the measured TDR echo and the theoretical TDR echo.
 3. The method of claim 2, wherein the measured TDR echo is a measured far-end echo, and the theoretical TDR echo is a theoretical far-end echo.
 4. The method of claim 1, wherein the updating step is based on a time shift and an equivalent TDR length.
 5. The method of claim 1, wherein the methodology is applicable single gauge straight loops, multi-section loops with different gauges and loops with bridged taps.
 6. A method comprising: estimating a physical loop length based on an equivalent TDR loop length and a time shift between a measured echo and an echo from an equivalent loop.
 7. A channel capacity estimation system comprising: means for obtaining a measured TDR echo; means for determining a theoretical TDR echo for a plurality of loop lengths; means for estimating the equivalent TDR length based on an optimization; means for updating the equivalent TDR length; and means for utilizing the updated TDR length to predict one or more of the upstream and downstream data rates.
 8. The system of claim 7, further comprising means for determining a time shift between the measured TDR echo and the theoretical TDR echo.
 9. The system of claim 8, wherein the measured TDR echo is a measured far-end echo, and the theoretical TDR echo is a theoretical far-end echo.
 10. The system of claim 7, wherein the updating is based on a time shift and an equivalent TDR length.
 11. The system of claim 7, wherein the system is adapted to estimate channel capacity for single gauge straight loops, multi-section loops with different gauges and loops with bridged taps.
 12. A system comprising: means for estimating a physical loop length based on an equivalent TDR loop length and a time shift between a measured echo and an echo from an equivalent loop.
 13. An information storage media having stored thereon information configured to estimate channel capacity comprising: information that obtains a measured TDR echo; information that determines a theoretical TDR echo for a plurality of loop lengths; information that estimates the equivalent TDR length based on an optimization; information that updates the equivalent TDR length; and information that utilizes the updated TDR length to predict one or more of the upstream and downstream data rates.
 14. An information storage media having stored thereon information configured to estimate a physical loop length based on an equivalent TDR loop length and a time shift between a measured echo and an echo from an equivalent loop.
 15. A channel capacity estimation system comprising: a TDR echo measurement module; a theoretical TDR echo determination module adapted to determine a theoretical TDR echo for a plurality of loop lengths; an equivalent TDR length estimation module adapted to estimate the equivalent TDR length based on an optimization; and an upstream and downstream data rate prediction module adapter to utilize an updated TDR length to predict one or more of the upstream and downstream data rates.
 16. The system of claim 15, further comprising a controller adapted to determine a time shift between a measured TDR echo and the theoretical TDR echo.
 17. The system of claim 16, wherein the measured TDR echo is a measured far-end echo, and the theoretical TDR echo is a theoretical far-end echo.
 18. The system of claim 15, wherein the system is adapted to estimate channel capacity for single gauge straight loops, multi-section loops with different gauges and loops with bridged taps.
 19. A system comprising a controller adapted estimate a physical loop length based on an equivalent TDR loop length, determined by an equivalent TDR length determination module, and a time shift between a measured echo and an echo from an equivalent loop. 